The Journal of Symbolic Logic

Research Article

An isomorphism between monoids of external embeddings: About definability in arithmetic

Mihai Prunescu

Institut Für Mathematik und Informatik, Universität Greifswald, Germany

Institute of Mathematics of the Romanian Academy, Bucharest, Romania, E-mail:


We use a new version of the Definability Theorem of Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.

(Received November 18 2000)

(Revised March 29 2001)